gcse linked pair pilot

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ADDITIONAL MATERIALS

A calculator will be required for this paper.

INSTRUCTIONS TO CANDIDATES

Use black ink or black ball-point pen.

Write your name, centre number and candidate numberin the spaces at the top of this page.

Answer all the questions in the spaces provided.

Take � as 3·14 or use the � button on your calculator.

INFORMATION FOR CANDIDATES

You should give details of your method of solutionwhen appropriate.

Unless stated, diagrams are not drawn to scale.

Scale drawing solutions will not be acceptable where you are asked to calculate.

The number of marks is given in brackets at the end of each question or part-question.

You are reminded that assessment will take into account the quality of written communication (including mathematical communication) used in your answer to question 3.

CJ*(S15-4362-02)

Surname

Other Names

CandidateNumber

0

CentreNumber

© WJEC CBAC Ltd.

GCSE LINKED PAIR PILOT

4362/02

APPLICATIONS OF MATHEMATICSUNIT 2: Financial, Business and Other ApplicationsHIGHER TIER

P.M. THURSDAY, 11 June 2015

2 hours

S15-4362-02

For Examiner’s use only

QuestionMaximum

MarkMark

Awarded

1. 6

2. 6

3. 6

4. 8

5. 9

6.(a) 8

6.(b) 3

7. 6

8.(a) 6

8.(b) 7

9. 12

10. 6

11.(a)(b) 13

11.(c) 4

Total 100

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2

Volume of prism = area of cross-section × length

Volume of sphere = �r3

Surface area of sphere = 4�r2

Volume of cone = �r2h

Curved surface area of cone = �rl

In any triangle ABC

Sine rule

Cosine rule a2 = b2 + c2 – 2bc cos A

Area of triangle = ab sin C

The Quadratic Equation

The solutions of ax2 + bx + c = 0

where a ≠ 0 are given by

length

cross-section

r

h

r

l

a

sin A

b

sin B

c

sin C= =

C

BA

a

c

b

xb b ac

a=

– ( – )± 2 4

2

Formula List

Area of trapezium = (a + b)h

b

h

a

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(4362-02) Turn over.

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Examineronly

© WJEC CBAC Ltd.

1. Lois lives in Llandudno. She is changing some pounds into other currencies before going on holiday in Europe.

The exchange rates are displayed below.

(a) Calculate how much Lois would receive in exchanging each of the following.

(i) £450 exchanged for Swiss francs. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . Swiss francs

(ii) £300 exchanged for Polish zloty. [2]

. . . . . . . . . . . . . . . . . . . . . . . . . . . Polish zloty

(b) How many pounds will Lois have to exchange to receive 363.60 euros? [2]

£ . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

Exchange £1 for

1.48 SF Swiss francs

1.20 € euros

5.04 Zl Polish zloty

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© WJEC CBAC Ltd.

2. Every Monday for 6 weeks, the number of customers entering a juice bar and the takings of the juice bar were recorded.

The takings were recorded correct to the nearest £10.

The table below shows the results.

Number ofcustomers

104 82 120 64 70 118

Takings (£) 480 390 560 290 310 530

(a) On the graph paper below, draw a scatter diagram of these results. [2]

50 60 70 80 90 100 110 120100

200

300

400

500

600

Takings (£)

Number of customers


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© WJEC CBAC Ltd.

(b) Draw, by eye, a line of best fit on your scatter diagram. [1]

(c) Estimate the takings for a Monday when there are 95 customers. [1]

(d) Approximately how much does a customer spend, on average, in the juice bar on a Monday? [2]

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3. You will be assessed on the quality of your written communication in this question.

© WJEC CBAC Ltd.

Jenna is saving for a summer holiday. She has already saved £45.

Jenna earns £250 per week. She plans to save 12% of the money she earns each week towards her holiday.

She has to pay a £100 deposit for the holiday in 2 weeks’ time. 12 weeks after paying her deposit, Jenna has to make a final payment of £365.

Show whether it is possible for Jenna to save enough to pay the deposit on time and make the final payment on time.

You must show all your working. [6]


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4.

The following section of a flowchart is used to find the membership fee for a snooker club.

Enter the person’s age, G, in years

Is G > 20?No

No

Yes

YesIs G < 60?

Membership feeis £12

Membership feeis £20

Membership fee,in £, is calculated

by 7G

10


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© WJEC CBAC Ltd.

(a) Use this section of the flowchart to find the membership fee for each of the following people.

Donald, aged 20 [1]

Dawn, aged 16 [1]

Shiona, aged 52 [2]

(b) Shiona, aged 52, has a younger brother Marc, aged 42. How much less does Marc have to pay to be a member of the snooker club than his sister

Shiona? [2]

(c) At what age does the membership fee become more expensive than the membership fee for a 60 year-old?

You must show your working. [2]

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© WJEC CBAC Ltd.

5. A retail index number is calculated by looking at increases or decreases in price over a period of time.

A loaf of bread that cost £1.60 on 1st January last year, costs £2.00 on 1st January this year.

The index number for this year’s cost of a loaf of bread, based on last year’s cost, is calculated as follows:

Index number = 2.00 × 100

1.60

= 125

(a) The index number for this year’s cost of bananas, based on last year’s cost, is 140.

(i) Has the cost of bananas increased more or less steeply than the cost of a loaf of bread?

You must give a reason for your answer. [1]

(ii) For this year’s costs, are you able to tell from the information given whether 1 kg of bananas is cheaper or more expensive than a loaf of bread?

You must give a reason for your answer. [1]


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(b) Below is last year’s cost of a basket of shopping. The index number for calculating this year’s cost, based on last year’s cost, is also given.

Item Cost last yearIndex number for calculating this year’s

cost based on last year’s cost

Box of teabags £2.36 110

Box of eggs £2.40 105

Carton of milk 90p 120

Carton of orange juice £1.10 90

Calculate the total cost of this basket of shopping for this year. Give your final answer correct to the nearest 10 pence. [4]

(c) A litre tub of ice cream now costs £2.36. The index number for the cost of a litre tub of ice cream based on last year’s cost is 97. What was the cost of a litre tub of ice cream last year? [3]

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6. Gareth spends some time looking at his outgoings and his savings.

(a) Gareth is trying to estimate the total cost of the electricity he uses over a 90-day period.

Last year he used 550 units of electricity during a 90-day period. The cost of electricity was 16p per unit. The standing charge was 30p per day. VAT was charged at 5%.

For a similar 90-day period this year Gareth estimates that • he will use the same quantity of electricity, • the cost of electricity per unit will rise by 12%, • the standing charge will rise by 8%, • VAT will be charged at 5%.

His sister has said that this will mean a 9% rise in the total cost of his electricity.

By calculating the actual increase in the total cost that Gareth is estimating for this 90-day period, find out whether Gareth’s sister has made a reasonable statement.

You must show all your working. [8]

© WJEC CBAC Ltd.


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(b) Gareth decides to invest £3000 in a savings bond offering a fixed rate of 1·25% per annum.

The investment company provides information stating how much the bond will be worth after 5, 15 and 25 years.

Gareth has lost the details so he decides to create his own table.

Complete Gareth’s table below, giving your answers correct to the nearest penny. [3]

© WJEC CBAC Ltd.

After5 years

After15 years

After25 years

£3000 bondis worth £. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . £. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . £. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7. (a) Ursula is designing data collection sheets.

She needs to decide on suitable groups for collecting her data.

The data she is collecting is as follows: • European shoe sizes, with none smaller than 32 and none greater than 46. • Lengths of shoe laces, with no measurement less than 30 cm and no measurement

greater than 88 cm.

For each data collection sheet, Ursula has decided she must have at least 5 groups all of equal width.

The outlines of Ursula’s data collection sheets are given below. Complete the first columns of these data collection sheets to show suitable groups. [4]

© WJEC CBAC Ltd.

European shoe size Tally Frequency

Length of shoe lace (cm) Tally Frequency


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(b) Luc has been recording ‘hours of sunshine’ each day.

The table below shows Luc’s data collection so far.

© WJEC CBAC Ltd.

Hours of sunshine Frequency

None

Less than an hour

More than an hour √ √

More than 2 hours √ √

More than 3 hours √

(i) Griff looks at Luc’s table and says:

“Looks to me like Luc has been recording hours of sunshine for five days.”

Explain why Griff could be correct. [1]

(ii) Sara looks at Luc’s table and says:

“Looks to me like Luc has been recording hours of sunshine for just two days.”

Explain why Sara could be correct. [1]

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8. (a) An organic fruit farm sells cherries and raspberries.

© WJEC CBAC Ltd.

Poppy buys 3 kg of cherries and 5 kg of raspberries. Harry buys 4 kg of cherries and 7 kg of raspberries. Poppy spends £66.10 and Harry spends £91.

Use an algebraic method to calculate the total cost of 10 kg of cherries and 1 kg of raspberries.


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(b) The organic fruit farm also sells gooseberries and blackcurrants. Gooseberries sell for £8.20 per kg. Blackcurrants sell for £10.80 per kg. An incomplete section of the spreadsheet used to enter sales of fruit is given below.

© WJEC CBAC Ltd.

(i) What amounts should be entered in cells C2 and C3? [1]

(ii) Why do you think the spreadsheet is designed so that amounts can be entered in cells C2, C3, C4 and C5? [1]

(iii) Complete the value of each entry for F10, G10, F11 and G11 in the spreadsheet above. [2]

(iv) Haf intends to buy some of all 4 types of fruit. Write down the formulae that would be used to calculate the amounts for cells F12

and G12.

F12 [2]

G12 [1]

A B C D E F G

1

2 Prices Cherries ...............

3 Raspberries ...............

4 Gooseberries 8.20

5 Blackcurrants 10.80

6

7 Customer Cherries Raspberries Gooseberries Blackcurrants Spend Total

8 Poppy 3 5 0 0 66.10 66.10

9 Harry 4 7 0 0 91.00 157.10

10 Gemma 0 0 3 2 .... ....

11 Nia 0 0 5 3 .... ....

12 Haf .... .... .... .... .... ....

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Examineronly9. Ben and Catrin both buy new fleece jackets.

© WJEC CBAC Ltd.

The label inside Ben’s jacket says:

The label inside Catrin’s jacket says:

Astra Jacket90% Polyester, 10% ElastaneSoft fleece fabric 180 g/m2

Snug Jacket80% Polyester, 20% Elastane

Stretchy fleece fabric 140 g/m2

Ben and Catrin know the following facts about their jackets. • Ben’s jacket weighs 234 g. • Catrin’s jacket is made with 8% less fleece fabric than Ben’s jacket.

(a) How much does Catrin’s Snug Jacket weigh? You must show your working. [4]


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Examineronly (b) The density of the fleece fabric in Snug Jackets is actually 140 g/m2, correct to the nearest

2 g/m2. This fabric is sold to the makers of the jackets on cardboard rolls. A cardboard roll with fleece fabric on it weighs 4·5 kg. The empty cardboard roll weighs 360 g.

© WJEC CBAC Ltd.

Complete the following sentence by inserting a correct value, accurate to 4 significant figures.

The roll contains at least ......................... m2 of Snug Jacket fleece fabric.


(c) A different roll contains 45 m2 of fleece fabric. This roll of fleece fabric has a label attached giving the area of fabric in cm2, written in

standard form. Complete the label below. You must show your working. [2]

Fleece fabric

Cardboard roll

45 m2 is ............................ cm2,written in standard form

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10. A garden centre sells plastic plant pots and saucers.

© WJEC CBAC Ltd.

The garden centre manager says that last week • the total number of plant pots and saucers sold was less than 3500 and • more than £500 was taken from sales of plant pots and saucers.

Let P represent the number of plant pots sold. Let S represent the number of saucers sold.

(a) Write down two inequalities, in terms of P and S, that satisfy the information given by the garden centre manager. [2]

(b) Use the graph paper opposite to find a region that is satisfied by your inequalities. You must clearly indicate your region. [3]

Plant pots cost £0.45 each. Saucers cost £0.20 each.


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(c) The following statement was made by a sales assistant about the sales of plant pots and saucers last week.

“800 plant pots and 1500 saucers were sold.”

Use your graph to complete the following table to indicate whether the statement could be true or not.

You must show on your graph how you justify your decision. [1]

© WJEC CBAC Ltd.

StatementCould be true?

Yes or No

800 plant pots and 1500 saucers were sold......................

00

1000

2000

3000

4000

1000 2000 3000 4000

S

P

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Examineronly11. BuildGen makes roof turrets for apartment blocks.

© WJEC CBAC Ltd.

(a) BuildGen is building a turret in the shape of a square-base pyramid. The frame for the turret is made using metal rods. An outline of the frame is shown below.

Diagram not drawn to scale

(i) BuildGen has ordered two packs of metal rods. Each pack contains 4 metal rods. One pack contains rods of length 6 m and the other pack contains rods of length

10 m. No rods are cut. Calculate the angle between the diagonal BD and the rod DP. [6]

P

A

B

D

C


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Examineronly (ii) The four slanting faces of the turret are to be tiled.

Calculate the total area to be covered in tiles. [4]

(b) BuildGen also builds turrets in the shape of a cone.

© WJEC CBAC Ltd.

This turret has a perpendicular height of 4 m.

The volume of the turret is 122 m3. Calculate the radius of this turret. [3]

perpendicularheight

4 m

radius

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(c) BuildGen makes similar-shaped turrets, by enlarging the lengths of the rods in the frame by the same scale factor.

© WJEC CBAC Ltd.

Diagram not drawn to scale

The diagram shows an example where BuildGen have enlarged all the lengths of the rods in the smaller frame by a scale factor of 1·6.

The area of each of the panels in the smaller frame is 4·6 m2. The internal volume of the larger frame is 76·2 m3.

Calculate

(i) the area of each of the panels in the larger frame, [2]

(ii) the internal volume of the smaller frame. [2]

END OF PAPER 4

gcse linked pair pilot

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